Which Tuple Relation calculus query is correct?

Question

Schema

student (rollNo, name, degree, year, sex, deptNo, advisor)
course (courseId, cname, credits, deptNo)
enrollment (rollNo, courseId, sem, year, grade)

Obtain the names of courses enrolled by student named Mahesh
{c.name | course(c) ^
               (∃s) (∃e) ( student(s) ^ enrollment(e)^ s.name = “Mahesh”^ s.rollNo= e.rollNo^ c.courseId = e.courseId) }

Do we really need (∃s) (∃e) ? Can the query be like:
{c.name | course(c) ^
                enrollment(e) ^
                student(s) ^
                c.courseId = e.courseId ^
                e.rollNo = s.rollNo ^
                s.name = "Mahesh" }

Are both correct?

Comments

@arjun sir can I get precise point why second query is incorrect. I dont get it even from the answers given here.

Answer 1

i think (a) is correct way

we have two types of variable free and bound

c is a free variable here, and we bound e as well s.

Comments

I know what are free and bound variables. What you are telling is explanation of quantifiers, free variables and bound variables. What I was asking is if using quantifiers themselves is mandatory for this query. Or to rephrase it, why we need to make courses and students a bounded variable? Please, can you bit more precise?

Answer 2

The second query describes the conditons for all students, for all courses and for all enrollments.

Comments

Yes I guess you are right. To generalize the facts:
The first query involves quantifiers.
And in general any relational algebra query which has quantifiers involved has implicit SQL DISTINCT clause applied (due to their nature).

The second query does not have any such clause, thus such queries does not have implicit SQL DISTINCT clause applied.

The next question arise is if their is any other stuffs for which DISTINCT is auto applied. I guess set operations (only intersection?) also have implicit SQL DISTINCT applied.

I tried running following queries and which indeed gives two tuples:

CREATE TABLE student (rollNo int, name varchar,degree varchar,year int, sex varchar, deptNo int, advisor varchar)
CREATE TABLE course (courseId int, cname varchar,credits float, deptNo int)
CREATE TABLE enrollment (rollNo int, courseId int,sem int, year int, grade char)

INSERT INTO student (rollNo,name) VALUES (1, "Mahesh Rajput")
INSERT INTO student (rollNo,name) VALUES (2, "Mahesh Singh")

INSERT INTO course (courseId, cname) VALUES (1,"DBMS")

INSERT INTO enrollment (rollNo, courseId) VALUES (1,1)

SELECT * FROM student as s, enrollment as e, course as c
WHERE s.rollNo = e.rollNo
AND e.courseId = c.courseId
AND s.name LIKE "Mahesh%"

Hope someone confirm this...

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@Gate aspirant 10.
Confirmed. Its indeed giving 2 tuples. Thanks for the spoonfed query :)

 

I think the query for 1st tuple calculus query woud be something like this:

select * from course s
where 1<=( select count(*) from student as s, enrollment as e
  where s.name='Mahesh%';
 );

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ok that is not executing...dont know how exactly should quantifiers be translated to SQL...